Resolved Kinematics of Runaway and Field OB Stars in the Small Magellanic Cloud

While it is necessary to correct for the Wing's systemic motion to identify runaway stars, our data also clearly reveal that the Wing and Bar are kinematically distinct components, with a 3D offset of $64\pm 10\ \,\mathrm{km}\,{{\rm{s}}}^{-1}$. The Wing has been identified as the southeast component of the SMC, and extends ≳2° beyond our observed data set, merging with the Magellanic Bridge linking the SMC to the Large Magellanic Cloud (LMC). Previous work (e.g., Brück 1978; Dobbie et al. 2014) shows an older co-existing Wing stellar population having RVs similar to those of young stars. This suggests that our sample is a good tracer of the bulk motion of this region, but follow-up examination of Gaia PMs for red giant stars is needed to understand differentials between the old and young populations.

The dynamical state of the Wing provides a vital kinematic discriminant for dynamical models of the internal structure of the SMC, the recent encounter history of the Magellanic Clouds, and the formation of the Magellanic Bridge (e.g., Besla et al. 2012; Zivick et al. 2018). In particular, the Wing kinematics seen here are consistent with transverse motion along the Bridge toward the LMC, instead of perpendicular to the Bridge. This vividly confirms models for a recent, direct collision between the Clouds 100–200 Myr ago, for which gas velocities are expected to be aligned with the Bridge. In contrast, motions perpendicular to the Bridge are theoretically expected in a tidal stripping scenario of an SMC that did not collide with the LMC, allowing it to retain ordered rotation. The absence of perpendicular motion is consistent with the results of Zivick et al. (2018), who find little evidence of rotation in the SMC, which also supports the direct collision model.

As noted in Section 1, non-compact binaries that are runaway systems must result from the dynamical ejection mechanism. In addition to SB2s, non-compact binaries also can be identified as eclipsing binaries (EBs), which are given in the Optical Gravitational Lensing Experiment (OGLE)-III EB catalog for the SMC (Pawlak et al. 2016). Of the 315 stars, only 295 are covered by the OGLE-III survey, as the easternmost Wing region is excluded. Furthermore, it is also possible to identify binaries with a compact remnant as high-mass X-ray binaries (HMXBs), which are compiled by Haberl & Sturm (2016). Runaway HMXBs result from the SN acceleration mechanism. Stars found to be SB2, EB, and/or HMXB are indicated in Table 1.

In Table 2, we list the numbers of stars in each population, along with the mean and median ${v}_{\perp }$ and standard deviations σ for each binary population. The median Gaia errors in ${{\boldsymbol{v}}}_{\alpha },{{\boldsymbol{v}}}_{\delta },$ and ${v}_{\perp }$ for the sample are 22, 17, and 28 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, with standard deviations on the errors of 5, 3, and 6 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively; thus the errors are more than a factor of 2 below the respective observed ${\sigma }_{\alpha },{\sigma }_{\delta },$ and ${\sigma }_{\perp }$. Therefore, these standard deviations reflect actual velocity dispersions convolved with the substantial errors. Figure 2 compares PM and RV for the 207 stars that also have RVs reported by Lamb et al. (2016), omitting the stars near the Wing-Bridge boundary. Stars shown by triangles and squares are, respectively, systemic RVs estimated from our multi-epoch monitoring surveys of the Bar (Table 3 of Lamb et al. 2016) and Wing region (ongoing). We caution that the single-epoch observations often include significant binary motions. Figure 2 confirms that the measured PMs and RVs are comparable. It is apparent that the PMs show a larger spread in R.A. than decl., which is due to the asymmetric Gaia errors (e.g., Gaia Collaboration et al. 2018). Thus, velocities, especially large ones, for any given star may not be real, but the kinematics of subsamples may be compared. We have also inspected the OGLE-III (Udalski et al. 2008) images available for 304 of our target stars to evaluate point-spread function (PSF) asymmetry and crowding, which can degrade the astrometry; stars that may be thus affected are flagged in Table 1. Measured ${v}_{\perp }$ have no apparent dependence on PSF asymmetry when flagging those with ≳10% variation in R.A. versus decl. But whereas ∼10% of all targets have neighbors within 15, targets having ${v}_{\perp }\gt 1{\sigma }_{\perp }$ are much more likely (24%, 10 out of 41) to have such close neighbors. Thus we caution that stars with ${v}_{\perp }\gtrsim 200\ \,\mathrm{km}\,{{\rm{s}}}^{-1}$ are likely dominated by spurious values (e.g., Platais et al. 2018).

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Table 2.  Kinematics of Binary SMC Field OB Stars

	Unclassifieda	EB	SB2	HMXB	Total
Number	267	16b	10b	15	304
${\sigma }_{\perp }/\mathrm{km}\,{{\rm{s}}}^{-1}$ c	43	42	45	23	42
${\sigma }_{\alpha }/\mathrm{km}\,{{\rm{s}}}^{-1}$	56	52	47	32	55
${\sigma }_{\delta }/\mathrm{km}\,{{\rm{s}}}^{-1}$	37	33	42	26	37
Median(${v}_{\perp }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	44	39	38	38	43
Mean(${v}_{\alpha }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	–3	16	16	1	–1
Mean(${v}_{\delta }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	7	8	–25	9	6
${\sigma }_{\mathrm{loc},\perp }/\mathrm{km}\,{{\rm{s}}}^{-1}$ c	42	51	34	21	41
${\sigma }_{\mathrm{loc},\alpha }/\mathrm{km}\,{{\rm{s}}}^{-1}$	53	50	42	31	52
${\sigma }_{\mathrm{loc},\delta }/\mathrm{km}\,{{\rm{s}}}^{-1}$	35	33	37	23	35
Median(${v}_{\mathrm{loc},\perp }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	39	29	50	31	39
Mean(${v}_{\mathrm{loc},\alpha }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	10	11	33	17	10
Mean(${v}_{\mathrm{loc},\delta }/\mathrm{km}\,{{\rm{s}}}^{-1}$)	3	2	–29	–4	2

Notes.

^aIncludes unidentified binaries. ^bThere are four stars identified as both EB and SB2. ^cValues for ${\sigma }_{\perp }$ and ${\sigma }_{\mathrm{loc},\perp }$ are standard deviations from the median.

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Figure 3(a) shows ${v}_{\perp }$ distributions for the 304 stars, which exclude those near the Wing-Bar boundary. We also show the contribution of each binary population. The peak of the ${v}_{\perp }$ distribution occurs at the value corresponding to the median error of 28 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, reflecting the Gaia detection limit at G < 15. The median ${v}_{\perp }$ of 44 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$ is therefore significant, occurring in the runaway velocity regime, as the typical velocity dispersion in OB associations is ∼5 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (e.g., Mel'nik & Dambis 2017). Because half of the sample has ${v}_{\perp }$ greater than the median value, which in turn is larger than typical bound velocity dispersions, this therefore implies that well over half of the sample corresponds to unbound runaways, as many unbound stars also occur at velocities below the median (e.g., Renzo et al. 2018).

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The population of "unclassified" stars in Table 2 simply refers to the remainder of the sample excluded by the other categories, and therefore includes any unidentified binaries. Thus, the EB, SB2, and HMXB populations are lower limits on the true numbers of non-compact and compact binary systems. Table 2 identifies 22 non-compact systems and 15 compact ones. We caution that the field includes a likely substantial population of non-runaway stars that formed in situ (e.g., Oey et al. 2013); analysis of the binary frequencies will be presented in a future work. Figure 3 and Table 2 show that the kinematics of the EB and SB2 populations are generally consistent with those of the total population, showing similar transverse velocity dispersions. In contrast, the spreads for the HMXBs are much lower, with the non-compact binaries having values about 50% larger than for the HMXBs. In fact, none of the HMXBs have ${v}_{\perp }\gt 1\sigma$ from the median of the total sample (Figure 3(a)). We caution that one SB2 with velocity >1σ, star 76253, has another star within 15 to the north, which may affect the Gaia astrometry (Table 1).

The above kinematics are derived from only two assumed systemic components, Wing and Bar, as described in Section 2. As there may be additional, higher-order systemic motions, we also examine the PMs of our sample stars relative to their local velocity fields. We use the Gaia PMs of stars from the Massey (2002) catalog of OB stars within a 5' (90 pc) radius of the target star to obtain the mean local velocity of the young population. We fitted the local PM distributions in R.A. and decl. with gaussians having σ = 45 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and 55 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively; these are the mean values for the Bar. The local transverse velocities ${v}_{\mathrm{loc}}$ obtained in this way are given in Table 1. Figure 3(b) and Table 2 show the resulting residual PM kinematics. We see a similar pattern as before, with the HMXBs again showing smaller standard deviations ${\sigma }_{\mathrm{loc}}$ when measured relative to the local fields.

We caution that K-S tests show that the difference between the ${v}_{\perp }$ distributions of the binary populations is not statistically significant. However, our sample likely contains a substantial, perhaps even dominant, contribution from non-runaway field stars that formed in situ (Oey et al. 2013; Lamb et al. 2016), which will significantly dilute the non-compact binary population in our sample at the lowest velocities. The fact that our HMXBs have smaller velocity dispersions than non-compact binaries is consistent with the expectation that bound compact binaries represent systems with less energetic SN kicks that failed to unbind the components. Moreover, dynamical ejections from dense clusters can accelerate runaways to higher velocities than the SN mechanism, because cluster acceleration can leverage the gravitational energy from multiple stars. Models by, for example, Brandt & Podsiadlowski (1995) and Renzo et al. (2018) show that HMXBs have runaway velocities <100 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, and typically half of that value, depending on the assumed kick velocities and pre-SN orbital parameters. In contrast, Perets & Šubr (2012) found that dynamically ejected runaways from clusters having masses on the order of ${10}^{4}\ \,{{\rm{M}}}_{\odot }$ can reach 200 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$, including significant fractions of binaries.

Despite contamination from non-runaways systems, the non-compact binaries show velocity distributions that are not only larger than for the HMXBs, but also similar to that for unclassified field OB stars (Table 2). The latter include single-star runaways from both mechanisms, so this suggests that dynamically ejected objects dominate over in situ field stars in the SMC. Furthermore, Renzo et al. (2018) predicted that ∼14% of post-SN binaries fail to disrupt, of which some fraction are observed as HMXBs. They also expect ∼3% of post-SN binaries to generate single runaways faster than 30 $\,\mathrm{km}\,{{\rm{s}}}^{-1}$. These estimates have large uncertainties, so we might expect roughly similar numbers of these two groups. However, there are only 15 HMXBs, whereas roughly half (134) of unclassified stars are fast runaways (median ${v}_{\perp }=44\ \,\mathrm{km}\,{{\rm{s}}}^{-1}$). While these numbers are subject to various biases, the large disparity does suggest that dynamical ejections likely dominate. We will examine additional properties, including frequencies, masses, and rotation of these field OB runaways in future work.